2. (Finding the present value of an annuity with growth.) Your firm is considering an investment which will require an immediate outlay of $1 million (Date 0) and generates monthly cash flows for the next 50 months (from Date 1 to Date 50). The first cash flow from this project is $10,000 and occurs one month from now (Date 1). Each subsequent cash flow is 1.5% larger than the previous cash flow. For example the date 2 cash flow is 1.5% larger than the date 1 cash flow. The last cash flow occurs at Date 50. After the 50 month time period, the plant producing the product in question will be useless and have no salvage value. The interest rate is 1.75% per month. Should make the investment? You could use brute force and calculate all 50 entries, or you could treat this as an annuity with growth! Calculate all values below to their exact dollar value. Do not round off or approximate. Consider the following plan of attack:

a) Calculate the present value of a perpetuity with cash flow of $10,000 starting in a month that grows at 1.5% a month when the interest rate per month is 1.75%. Call this value PVfront.

b) Calculate the cash flow in month 51 of the perpetuity in (a). Call this C51.

c) Find the present (month 0) value of the perpetuity that pays nothing until month 51 when it pays C51 and has payments each month thereafter that grow at a rate of 1.5% a month with the monthly interest rate being 1.75%. Call this value PVtail.

d) Calculate PVfront - PVtail. What does this have to do with the problem stated in the first paragraph? e) Should you make the investment?